pwm.ub {lmomco} | R Documentation

## Unbiased Sample Probability-Weighted Moments

### Description

Unbiased sample Probability-Weighted Moments (PWMs) are computed from a sample. The first five β_r's are computed by default.

β_r = n^{-1} {n-1 choose r}^{-1} sum^n_{j=1} (j-1 choose r)x_{j:n}

### Usage

    pwm.ub(x,nmom=5,sort=TRUE)

### Arguments

`x` | A vector of data values.
`nmom` | Number of PWMs to return.
`sort` | Does the data need sorting? The computations require sorted data. This option is provided to optimize processing speed if presorted data already exists.

### Value

An R `list` is returned.

`betas` | The PWMs. Note that convention is the have a β_0, but this is placed in the first index `i=1` of the `betas` vector.
`source` | Source of the PWMs: “pwm.ub”

### Author(s)

W.H. Asquith

### References

Greenwood, J.A., Landwehr, J.M., Matalas, N.C., and Wallis, J.R., 1979, Probability weighted moments—Definition and relation to parameters of several distributions expressable in inverse form: Water Resources Research, vol. 15, p. 1,049–1,054.

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

### See Also

`pwm.pp`, `pwm.gev`, `pwm2lmom`

### Examples

    pwm <- pwm.ub(rnorm(20))

[Package lmomco version 0.92 Index]